**1) A tour of G is a closed walk of graph G which includes every edge G at least once. A ..... tour of G is a tour which includes every edge of G exactly once ?**

- Hamiltonian
- Planar
- Isomorphic
- Euler

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**Answer = D**

**Explanation: If some closed walk in a graph contains all the edges then the walk is called Euler.**

**2) Which of the following is not a type of graph ?**

- Euler
- Hamiltonian
- Tree
- Path

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**Answer = D**

**Explanation:Path is a way from one node no another but not a graph.**

**3) Choose the most appropriate definition of plane graph ?**

- A graph drawn in a plane in such a way that any pair of edges meet only at their end vertices
- A graph drawn in a plane in such a way that if the vertex set of graph can be partitioned into two non - empty disjoint subset X and Y in such a way that each edge of G has one end in X and one end in Y.
- A simple graph which is Isomorphic to Hamiltonian graph
- None of these

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**Answer = A**

**Explanation: No explanation for this question.**

**4) A continuous non - intersecting curve in the plane whose origin and terminus coincide ?**

- Planer
- Jordan
- Hamiltonian
- All of these

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**Answer = B**

**Explanation: The jordan graph is the set of all vertices of minimum eccentricity that is the set of all vertices A where the greatest distance to other vertex B is minimal.**

**5) Polyhedral is.... ?**

- A simple connected graph
- A plane graph
- A graph in which the degree of every vertex and every face is atleast 3
- All of above

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**Answer = D**

**Explanation: A polyhedral graph is the undirected graph formed from the vertices and edges of a convex polyhedron**

**6) A path in graph G, which contains every vertex of G once and only once ?**

- Eulartour
- Hamiltonian Path
- Eular trail
- Hamiltonian tour

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**Answer = B**

**Explanation:A Hamiltonian circuit in a connected graph is defined as a closed walk that traverse every vertex of G exactly once except the starting vertex.**

**7) A minimal spanning tree of a graph G is.... ?**

- A spanning sub graph
- A tree
- Minimum weights
- All of above

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**Answer = D**

**Explanation: A tree is said to be spanning tree of connected graph G if it is subgraph of G and contains all the vertices of G.**

**8) A tree having a main node, which has no predecessor is.... ?**

- Spanning tree
- Rooted tree
- Weighted tree
- None of these

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**Answer = B**

**Explanation:A tree in which one vertex distinguish from all other is called rooted tree.**

**9) Diameter of a graph is denoted by diam(G) is defined by.... ?**

- max (e(v) : v belongs to V)
- max( d(u,v) )
- Both A and B
- None of these

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**Answer = C**

**Explanation: The diameter of a graph G is largest distance between two vertices in a graph G.**

**10) A vertex of a graph is called even or odd depending upon ?**

- Total number of edges in a graph is even or odd
- Total number of vertices in a graph is even or odd
- Its degree is even or odd
- None of these

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**Answer = C**

**Explanation: The vertex of a graph is called even or odd based on its degree.**

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